We present the discovery of a giant \gtrsim 100 kpc Ly \alpha nebula detected in the core of the X-ray emitting cluster CL J1449+0856 at z = 1.99 through Keck/LRIS narrow-band imaging .
This detection extends the known relation between Ly \alpha nebulae and overdense regions of the Universe to the dense core of a 5 - 7 \times 10 ^ { 13 } M _ { \odot } cluster .
The most plausible candidates to power the nebula are two Chandra-detected AGN host cluster members , while cooling from the X-ray phase and cosmological cold flows are disfavored primarily because of the high Ly \alpha to X-ray luminosity ratio ( L _ { \mathrm { Ly \alpha } } / L _ { \mathrm { X } } \approx 0.3 , \gtrsim 10 - 1000 \times higher than in local cool-core clusters ) and by current modeling .
Given the physical conditions of the Ly \alpha -emitting gas and the possible interplay with the X-ray phase , we argue that the Ly \alpha nebula would be short-lived ( \lesssim 10 Myr ) if not continuously replenished with cold gas at a rate of \gtrsim 1000 M _ { \odot } yr ^ { -1 } .
We investigate the possibility that cluster galaxies supply the required gas through outflows and we show that their total mass outflow rate matches the replenishment necessary to sustain the nebula .
This scenario directly implies the extraction of energy from galaxies and its deposition in the surrounding intracluster medium , as required to explain the thermodynamic properties of local clusters .
We estimate an energy injection of the order of \thickapprox 2 keV per particle in the intracluster medium over a 2 Gyr interval .
In our baseline calculation AGN provide up to 85 % of the injected energy and 2/3 of the mass , while the rest is supplied by supernovae-driven winds .